Negation and Paraconsistent Logics |
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Authors: | Soma Dutta Mihir K Chakraborty |
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Institution: | 1. Indian Institute of Bio-Social Research and Development, Prafulla Kanan, VIP Road, Kestopur, Kolkata, 700101, India 2. Jadavpur University, Kolkata, India 3. Indian Statistical Institute, Kolkata, India
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Abstract: | Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present
in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation (?{\neg}) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During
this study two points have come out. The first one is that the notion of inconsistency of paraconsistent logics turns out
to be a formula-dependent notion and the second one is that the characterization (i.e. equivalence) appears to be pertinent
to a class of paraconsistent logics which have double negation property. |
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